Theorem imaeq2d 3410

Description: Equality theorem for image. (Contributed by FL, 15-Dec-2006.)

Hypothesis

Ref	Expression
imaeq1d.1	|- (ph -> A = B)

Assertion

Ref	Expression
imaeq2d	|- (ph -> (C"A) = (C"B))

Proof of Theorem imaeq2d

Step	Hyp	Ref	Expression
1		imaeq1d.1	. 2 |- (ph -> A = B)
2		imaeq2 3408	. 2 |- (A = B -> (C"A) = (C"B))
3	1, 2	syl 10	1 |- (ph -> (C"A) = (C"B))

Syntax hints:   -> wi 3   = wceq 958  "cima 3179

This theorem is referenced by:  hbimad 3418  csbima12g 3419  elimasng 3433  eliniseg 3435  fnex 3613  fveq2 3730  fsn2 3842  funfvima3 3860  isofrlem 3907  curry1 4104  eceq2 4284  mapsn 4351  cnconst 7777  metcnp 7884

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-11 969  ax-12 970  ax-13 971  ax-14 972  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462  ax-sep 2708  ax-pow 2748  ax-pr 2785

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-eu 1384  df-mo 1385  df-clab 1467  df-cleq 1472  df-clel 1475  df-ne 1590  df-v 1815  df-dif 2052  df-un 2053  df-in 2054  df-ss 2056  df-nul 2284  df-pw 2406  df-sn 2416  df-pr 2417  df-op 2420  df-br 2625  df-opab 2672  df-xp 3190  df-cnv 3192  df-dm 3194  df-rn 3195  df-res 3196  df-ima 3197

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